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Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size

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  • Elena Pesavento

Abstract

Numerous tests for integration and cointegration have been proposed in the literature. Since Elliott, Rothemberg and Stock (1996) the search for tests with better power has moved in the direction of finding tests with some optimality properties both in univariate and multivariate models. Although the optimal tests constructed so far have asymptotic power that is indistinguishable from the power envelope, it is well known that they can have severe size distortions in finite samples. This paper proposes a simple and powerful test that can be used to test for unit root or for no cointegration when the cointegration vector is known. Although this test is not optimal in the sense of Elliott and Jansson (2003), it has better finite sample size properties while having asymptotic power curves that are indistinguishable from the power curves of optimal tests. Similarly to Hansen (1995), Elliott and Jansson (2003), Zivot (2000), and Elliott, Jansson and Pesavento (2005) the proposed test achieves higher power by using additional information contained in covariates correlated with the variable being tested. The test is constructed by applying Hansen’s test to variables that are detrended under the alternative in a regression augmented with leads and lags of the stationary covariates. Using local to unity parametrization, the asymptotic distribution of the test under the null and the local alternative is analytically computed.

Suggested Citation

  • Elena Pesavento, 2006. "Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size," Economics Working Papers ECO2006/18, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2006/18
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    References listed on IDEAS

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    6. Hansen, Bruce E., 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1148-1171, October.
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    Cited by:

    1. Galvao Jr., Antonio F., 2009. "Unit root quantile autoregression testing using covariates," Journal of Econometrics, Elsevier, vol. 152(2), pages 165-178, October.
    2. Fossati, Sebastian, 2012. "Covariate unit root tests with good size and power," Computational Statistics & Data Analysis, Elsevier, pages 3070-3079.
    3. Sebastian Fossati, 2013. "Unit root testing with stationary covariates and a structural break in the trend function," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 368-384, May.
    4. Addison, John T. & Portugal, Pedro & Vilares, Hugo, 2015. "Unions and Collective Bargaining in the Wake of the Great Recession," IZA Discussion Papers 8943, Institute for the Study of Labor (IZA).
    5. Game Aaron & Wu Jason, 2013. "A Covariate Residual-Based Cointegration Test Applied to the CDS-Bond Basis," Journal of Time Series Econometrics, De Gruyter, vol. 5(2), pages 163-192, April.
    6. Christopoulos, Dimitris K. & León-Ledesma, Miguel A., 2008. "Time-series output convergence tests and stationary covariates," Economics Letters, Elsevier, vol. 101(3), pages 297-299, December.

    More about this item

    Keywords

    Unit Root Test; GLS detrending.;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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